Chapter 5: Q. 176 (page 523)

Explain why $- 5^{3} = (- 5)^{3}$ but $- 5^{4} \neq (- 5)^{4}$

Short Answer

Expert verified

This is correct only for odd exponents, for even exponents it is not correct.

Step by step solution

Given information

Explain why $(- 5)^{3} = - 5^{3}$ but $(- 5)^{4} \neq - 5^{4}$

Explanation

Here

$(- 5)^{3} = (- 1 \times 5)^{3} = (- 1)^{3} \times (5)^{3} = - 1 \times 5^{3} = - 5^{3}$

And

$(- 5)^{4} = (- 1 \times 5)^{4} = (- 1)^{4} \times (5)^{4} = 1 \times 5^{4} = 5^{4} \neq - 5^{4}$

This is correct only for odd exponents, for even exponents it is not correct.

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Explain why $- 5^{3} = (- 5)^{3}$ but $- 5^{4} \neq (- 5)^{4}$

Short Answer

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Explain why -53=(-5)3 but-54≠(-5)4

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Explain why $- 5^{3} = (- 5)^{3}$ but $- 5^{4} \neq (- 5)^{4}$