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3 years ago

Which expression is equivalent to the given expression?

Mathematics

2 answers:

mezya [45]3 years ago

7 0

<u>Choice C. </u><u>is equivalent.</u>

Let's first simplify, starting with the denominator.

a to the power of 0 is 1. —> any value to the power of 0 is 1.

That leaves us with <u>(</u>1b^2)^4. Now we can distribute the exponent. But before that, let's get rid of the coefficient 1, which isn't necessary.

Now we are left with (b^2)^4.

Let's use the power of the power rule, which means that we multiply the exponent by the exponent. The denominator is now b^8.

Looking at the numerator, there is a b, which has a hidden exponent of one. —> We can get rid of it by taking away its exponent of 1 with the b^8 from the denomiator.

. . . b^1 goes away, and b^8 becomes b^7.

<u>We cannot simplify any further,</u> therefore the final expression is. . .

Masja [62]3 years ago

3 0

Step-by-step explanation:

$( \frac{6ab}{(a {}^{0} {b}^{2} ) {}^{4} } ) \\ \\ =( \frac{6ab}{1 \times {b}^{8} } ) \\ \\ = \frac{6a}{ {b}^{7} }$

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A and B are complementary angles if angle a equals (X +24) and angle B equals (X +16) then what is the measurement of b

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3 years ago

Caden states that n^2 +3n + 2n is an equivalent expression to 6n. Why is Caden's statement incorrect?

malfutka [58]

$\begin{gathered} \text{The simplification of n}^2+3n+2n\text{ is:} \\ i)n^2+5n \\ By\text{ collecting common term, this can be written in form of:} \\ ii)\text{ n(n+5)} \end{gathered}$

Thus, options A and D hold, from the simplifications above.

Let's consider the validity of the remaining options provided.

$\begin{gathered} \text{For option B)} \\ \text{substitute for n=1 into the expression n}^2+3n+2n,\text{ we have} \\ 1^2+3(1)+2(1)=1+3+2=6 \\ \text{substitute for n=1 into the expression 6n, we have} \\ 6(1)=6 \\ \text{Thus, the expression n}^2+3n+2n\text{ is equivalent to 6n, for n=1} \end{gathered}$ $\begin{gathered} \text{For option C)} \\ \text{The expression n}^2+3n+2n\text{ does not simplify to 7n} \end{gathered}$ $\begin{gathered} \text{For option E)} \\ \text{substitute for n=4 into the expression n}^2+3n+2n,\text{ we have:} \\ 4^2+3(4)+2(4)=16+12+8=36 \\ \text{substitute for n=6 into the expression 6n, we have:} \\ 6(4)=24 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=4} \end{gathered}$ $\begin{gathered} \text{For option F)} \\ \text{substitute for n=3 into the expression n}^2+3n+2n,\text{ we have:} \\ 3^2+3(3)+2(3)=9+9+6=24 \\ \text{substitute for n=3 into the expression 6n, we have:} \\ 6(3)=18 \\ \text{Thus, the two(2) expressions are not equivalent to each other, for n=3} \end{gathered}$

Hence, the correct options that apply are options A, D, E and F

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1 year ago

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Step-by-step explanation:

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Which expression is equivalent to the given expression?​

Which expression is equivalent to the given expression?