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Popular >

simplify 45^{(-3)/2}*45^2

Solution

simplify

4 5^{\frac{- 3}{2}} \cdot 4 5^{2}

Solution

3 \cdot 5^{\frac{1}{2}}

+1

Decimal Notation

6.70820 \dots

Solution steps

4 5^{\frac{- 3}{2}} \cdot 4 5^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

4 5^{\frac{- 3}{2}} \cdot 4 5^{2} = 4 5^{\frac{- 3}{2} + 2}

= 4 5^{\frac{- 3}{2} + 2}

\frac{- 3}{2} + 2 = \frac{1}{2}

= 4 5^{\frac{1}{2}}

Prime factorization of

45 : 3^{2} \cdot 5

= (3^{2} \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

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

(3^{2} \cdot 5)^{\frac{1}{2}} = (3^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

= (3^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

(3^{2})^{\frac{1}{2}} = 3

= 3 \cdot 5^{\frac{1}{2}}

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Frequently Asked Questions (FAQ)

What is 45^{(-3)/2}*45^2 ?
The solution to 45^{(-3)/2}*45^2 is 3*5^{1/2}