What is \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3} ?

The solution to \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3} is (d+1)^{27}(6c+7)^9

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simplify \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3}

simplify

5 [(6 c + 7)^{15} (d + 1)^{45}]^{3}

(d + 1)^{27} (6 c + 7)^{9}

Solution steps

5 [(6 c + 7)^{15} (d + 1)^{45}]^{3}

Apply radical rule:

n a = a^{\frac{1}{n}}

= ([(6 c + 7)^{15} (d + 1)^{45}]^{3})^{\frac{1}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= [(6 c + 7)^{15} (d + 1)^{45}]^{3 \cdot \frac{1}{5}}

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

= [(6 c + 7)^{15} (d + 1)^{45}]^{\frac{3}{5}}

Apply exponent rule:

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

= ((d + 1)^{45})^{\frac{3}{5}} ((6 c + 7)^{15})^{\frac{3}{5}}

((6 c + 7)^{15})^{\frac{3}{5}} : (6 c + 7)^{9}

= (6 c + 7)^{9} ((d + 1)^{45})^{\frac{3}{5}}

((d + 1)^{45})^{\frac{3}{5}} : (d + 1)^{27}

= (6 c + 7)^{9} (d + 1)^{27}

4.63 e^{- 0.12 x}

e^{- \frac{1}{2} l n (2 x)}

1 + 5 \cdot 2

5 x^{3} \cdot x

- 2 \cdot e^{- \frac{- 2 ^{2}}{162}}

What is \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3} ?
The solution to \sqrt[5]{[(6c+7)^{15}(d+1)^{45}]^3} is (d+1)^{27}(6c+7)^9