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Popular >

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

Solution

simplify

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

Solution

\frac{1}{1000}

+1

Decimal Notation

0.001

Solution steps

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

1 0^{3} = 1000

= 1000 ((3 + 7)^{2})^{- 3}

Apply exponent rule:

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

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

= 1000 (3 + 7)^{2 (- 3)}

2 (- 3) = - 6

= 1000 (3 + 7)^{- 6}

Apply exponent rule:

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

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

= 1000 \cdot \frac{1}{( 3 + 7 ) ^{6}}

(3 + 7)^{6} = 1000000

= 1000 \cdot \frac{1}{1000000}

1000 \cdot \frac{1}{1000000} = \frac{1}{1000}

= \frac{1}{1000}

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Frequently Asked Questions (FAQ)

What is 10^3*[(3+7)^2]^{-3} ?
The solution to 10^3*[(3+7)^2]^{-3} is 1/1000