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How do you simplify # 7(x^4)^5 (-4x^2)^2#?

Answer 1

Savannah Anderson

#112x^24#

As #(x^m)^n=x^(mn)#,

#7(x^4)^5*(-4x^2)^2#

= #7x^(4*5)*(-4)^2*x^(2*2)#

= #7x^20*16*x^4#

= #112*x^(20+4)#

= #112x^24#

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Answer 2

Genesis Allen

To simplify (7(x^4)^5(-4x^2)^2), first apply the exponents to each term within the parentheses:

(7(x^{20})(16x^4))

Then, multiply the coefficients and combine the like terms:

(112x^{24})

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Answer 3

Kennedy Adams

To simplify (7(x^4)^5 (-4x^2)^2), you first apply the exponent rules to the terms inside the parentheses, then perform the multiplication:

(7(x^4)^5 = 7x^{4 \times 5} = 7x^{20})

((-4x^2)^2 = (-4)^2(x^2)^2 = 16x^{2 \times 2} = 16x^4)

Now, multiply the simplified terms:

(7x^{20} \times 16x^4 = 112x^{20 + 4} = 112x^{24})

So, (7(x^4)^5 (-4x^2)^2) simplifies to (112x^{24}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.