What is (4*10^{-5})^3 ?

The solution to (4*10^{-5})^3 is 1/(5^{15)*512}

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simplify (4*10^{-5})^3

simplify

(4 \cdot 1 0^{- 5})^{3}

\frac{1}{5 ^{15} \cdot 512}

Decimal Notation

6.4 E - 14

Solution steps

(4 \cdot 1 0^{- 5})^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(4 \cdot 1 0^{- 5})^{3} = 4^{3} (1 0^{- 5})^{3}

= 4^{3} (1 0^{- 5})^{3}

4^{3} = 64

= 64 (1 0^{- 5})^{3}

Apply exponent rule:

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

(1 0^{- 5})^{3} = 1 0^{- 5 \cdot 3}

= 64 \cdot 1 0^{- 5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= 64 \cdot 1 0^{- 15}

Apply exponent rule:

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

1 0^{- 15} = \frac{1}{1 0 ^{15}}

= 64 \cdot \frac{1}{1 0 ^{15}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 64}{1 0 ^{15}}

Multiply the numbers:

1 \cdot 64 = 64

= \frac{64}{1 0 ^{15}}

Factor

64 : 2^{6}

Factor

1 0^{15} : 2^{15} \cdot 5^{15}

= \frac{2 ^{6}}{2 ^{15} \cdot 5 ^{15}}

Cancel

\frac{2 ^{6}}{2 ^{15} \cdot 5 ^{15}} : \frac{1}{5 ^{15} \cdot 2 ^{9}}

= \frac{1}{5 ^{15} \cdot 2 ^{9}}

2^{9} = 512

= \frac{1}{5 ^{15} \cdot 512}

(x - 2)^{2} + 2 (x - 2) + 6

4 x^{3} - 19 x^{2} + 21 x

(\frac{- 2}{2})^{2}

560

- \frac{2}{3} \cdot \frac{1}{2}