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Popular >

simplify 10^4*[(7+3)^2]^{-3}

Solution

simplify

1 0^{4} \cdot [(7 + 3)^{2}]^{- 3}

Solution

\frac{1}{100}

+1

Decimal Notation

0.01

Solution steps

1 0^{4} ((7 + 3)^{2})^{- 3}

1 0^{4} = 10000

= 10000 ((7 + 3)^{2})^{- 3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

((7 + 3)^{2})^{- 3} = (7 + 3)^{2 (- 3)}

= 10000 (7 + 3)^{2 (- 3)}

2 (- 3) = - 6

= 10000 (7 + 3)^{- 6}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(7 + 3)^{- 6} = \frac{1}{( 7 + 3 ) ^{6}}

= 10000 \cdot \frac{1}{( 7 + 3 ) ^{6}}

(7 + 3)^{6} = 1000000

= 10000 \cdot \frac{1}{1000000}

10000 \cdot \frac{1}{1000000} = \frac{1}{100}

= \frac{1}{100}

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Frequently Asked Questions (FAQ)

What is 10^4*[(7+3)^2]^{-3} ?
The solution to 10^4*[(7+3)^2]^{-3} is 1/100