en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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}}

Popular Examples

simplify \sqrt[3]{25}*\sqrt[3]{5}simplify

∣ 3 x - 4 ∣ + 2 = 8

∣ x - 3 ∣ = 12

factor 2ln(+1)factor

2 ln (+ 1)

factor 25a^4b+10ab^2 factor

25 a^{4} b + 10 a b^{2}

Frequently Asked Questions (FAQ)

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