What is (\sqrt[3]{5^2*7})^8 ?

The solution to (\sqrt[3]{5^2*7})^8 is cube root of 7^2}*153125\sqrt[3]{5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (\sqrt[3]{5^2*7})^8

simplify

Decimal Notation

958152.85168 \dots

Solution steps

Apply exponent rule:

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

Apply exponent rule:

= (5^{2} \cdot 7)^{2} (5^{2} \cdot 7)^{\frac{2}{3}}

Apply exponent rule:

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

(5^{2} \cdot 7)^{2} (5^{2} \cdot 7)^{\frac{2}{3}} = (5^{2} \cdot 7)^{2 + \frac{2}{3}}

= (5^{2} \cdot 7)^{2 + \frac{2}{3}}

2 + \frac{2}{3} = \frac{8}{3}

= (5^{2} \cdot 7)^{\frac{8}{3}}

Apply exponent rule:

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

(5^{2} \cdot 7)^{\frac{8}{3}} = (5^{2})^{\frac{8}{3}} \cdot 7^{\frac{8}{3}}

= (5^{2})^{\frac{8}{3}} \cdot 7^{\frac{8}{3}}

7^{\frac{8}{3}} = 7^{2} \cdot 7^{\frac{2}{3}}

7^{2} = 49

Multiply the numbers:

49 \cdot 3125 = 153125

(2.8 \times 1 0^{- 4}) (16)^{1.08}

e^{- 0.02 \cdot 0.02617}

- 2 e^{- \frac{1}{2}}

t^{3} (3 t^{2})

What is (\sqrt[3]{5^2*7})^8 ?
The solution to (\sqrt[3]{5^2*7})^8 is cube root of 7^2}*153125\sqrt[3]{5