Exponents and Powers - Class 8 - Mathematics
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Examples - Exponents and Powers | NCERT | Mathematics | Class 8
Find the value of
(i) $2^{-3}$
(ii) $\frac{1}{3^{-2}}$
The values are as follows:
(i) $2^{-3} = \frac{1}{8} = 0.125$
(ii) $\frac{1}{3^{-2}} = 9$
Simplify
(i) $(-4)^{5} \times(-4)^{-10}$
(ii) $2^{5} \div 2^{-6}$
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Sign up nowExpress $4^{-3}$ as a power with the base 2.
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Sign up nowSimplify and write the answer in the exponential form.
(i) $\left(2^{5} \div 2^{8}\right)^{5} \times 2^{-5}$
(ii) $(-4)^{-3} \times(5)^{-3} \times(-5)^{-3}$
(iii) $\frac{1}{8} \times(3)^{-3}$
(iv) $(-3)^{4} \times\left(\frac{5}{3}\right)^{4}$
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Sign up nowFind $m$ so that $(-3)^{m+1} \times(-3)^{5}=(-3)^{7}$
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Sign up nowFind the value of $\left(\frac{2}{3}\right)^{-2}$.
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Sign up nowSimplify (i) $\left\{\left(\frac{1}{3}\right)^{-2}-\left(\frac{1}{2}\right)^{-3}\right\} \div\left(\frac{1}{4}\right)^{-2}$
(ii) $\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-5}$
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Sign up nowExpress the following numbers in standard form.
(i) 0.000035
(ii) 4050000
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Sign up nowExpress the following numbers in usual form.
(i) $3.52 \times 10^{5}$
(ii) $7.54 \times 10^{-4}$
(iii) $3 \times 10^{-5}$
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Sign up nowExercise 10.1 - Exponents and Powers | NCERT | Mathematics | Class 8
Evaluate.
(i) $3^{-2}$
(ii) $(-4)^{-2}$
(iii) $\left(\frac{1}{2}\right)^{-5}$
The evaluations are as follows:
(i) $3^{-2}$ is equal to $$\frac{1}{9}$$
(ii) $(-4)^{-2}$ is equal to $$\frac{1}{16}$$
(iii) $\left(\frac{1}{2}\right)^{-5}$ is equal to $$32$$
Simplify and express the result in power notation with positive exponent.
(i) $(-4)^{5} \div(-4)^{8}$
(ii) $\left(\frac{1}{2^{3}}\right)^{2}$
(iii) $(-3)^{4} \times\left(\frac{5}{3}\right)^{4}$
(iv) $\left(3^{-7} \div 3^{-10}\right) \times 3^{-5}$
(v) $2^{-3} \times(-7)^{-3}$
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Sign up nowFind the value of
(i) $\left(3^{\circ}+4^{-1}\right) \times 2^{2}$
(ii) $\left(2^{-1} \times 4^{-1}\right) \div 2^{-2}$
(iii) $\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}$
(iv) $\left(3^{-1}+4^{-1}+5^{-1}\right)^{0}$$\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}$
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Sign up nowEvaluate (i) $\frac{8^{-1} \times 5^{3}}{2^{-4}}$
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Sign up nowFind the value of $m$ for which $5^{m} \div 5^{-3}=5^{5}$.
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Sign up nowEvaluate (i) $\left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}$ (ii) $\left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4}$
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Sign up nowSimplify.
(i) $\frac{25 \times t^{-4}}{5^{-3} \times 10 \times t^{-8}}(t \neq 0)$
(ii) (ii) $\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}$
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Sign up nowExercise 10.2 - Exponents and Powers | NCERT | Mathematics | Class 8
Express the following numbers in standard form.
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
The numbers expressed in standard form are as follows:
(i) $0.0000000000085$ in standard form is $8.5*10^{-12}$.
(ii) $0.00000000000942$ in standard form is $9.42*10^{-12}$.
(iii) $6020000000000000$ in standard form is $6.02*10^{15}$.
(iv) $0.00000000837$ in standard form is $8.37*10^{-9}$.
(v) $31860000000$ in standard form is $3.186*10^{10}$.
Express the following numbers in usual form.
(i) $3.02 \times 10^{-6}$
(ii) $4.5 \times 10^{4}$
(iii) $3 \times 10^{-8}$
(iv) $1.0001 \times 10^{9}$
(v) $5.8 \times 10^{12}$
(vi) $3.61492 \times 10^{6}$
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Sign up nowExpress the number appearing in the following statements in standard form.
(i) 1 micron is equal to $\frac{1}{1000000} \mathrm{~m}$.
(ii) Charge of an electron is $0.000,000,000,000,000,000,16$ coulomb.
(iii) Size of a bacteria is $0.0000005 \mathrm{~m}$
(iv) Size of a plant cell is $0.00001275 \mathrm{~m}$
(v) Thickness of a thick paper is $0.07 \mathrm{~mm}$
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Sign up nowIn a stack there are 5 books each of thickness $20 \mathrm{~mm}$ and 5 paper sheets each of thickness $0.016 \mathrm{~mm}$. What is the total thickness of the stack?
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Sign up nowExtra Questions - Exponents and Powers | NCERT | Mathematics | Class 8
If $0.00000000837$ is expressed as $x.37 \times 10^y$, then $y \times 10^x$ written as a numeral is
Option A) $8 \times 10^9$
Option B) $-9 \times 10^8$
Option C) $-8 \times 10^9$
Option D) $9 \times 10^8$
First, let's express the number $0.00000000837$ in scientific notation. We need to adjust the decimal point such that there is one non-zero digit to the left of the decimal. The number $0.00000000837$ can be rewritten as:
$$ 8.37 \times 10^{-9} $$
This transformation moves the decimal point 9 places to the right and thus employs the exponent of $-9$.
According to the given expression format $x.37 \times 10^y$, we match to:
$x = 8$
$y = -9$
Now, we need to calculate $y \times 10^x$:
$$ y \times 10^x = (-9) \times 10^8 $$
Thus, looking at the provided options, Option B) $-9 \times 10^8$ is correct.
a
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Sign up nowIf $m$ and $n$ are integers, $a$ is a non-zero integer and $a^{m} \times a^{n} = a^{x}$, then the value of $x$ is:
A) $mn$
B) $m + n$
C) $m - n$
D) $\frac{m}{n}$
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