Question

Which expression is equivalent to 144^3/2

Answer 1

Answer:

$\large\boxed{144^\frac{3}{2}=1728}$

Step-by-step explanation:

$\sqrt[n]{a^m}=a^\frac{m}{n}\\\\144^\frac{3}{2}=144^{1\frac{1}{2}}=144^{1+\frac{1}{2}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=144^1\cdot144^{\frac{1}{2}}=144\sqrt{144}=144\cdot12=1728$

Answer 2

Simplify using $a\frac{n}{m} =\sqrt[m]{a^{n} } =\sqrt{144^{3} }$

Now, we will factor it and rewrite the radicand in exponential form:

                                  $\sqrt{144^{2}*144 }$

Rewrite the expression using:

$\sqrt[n]{ab} =\sqrt[n]a}*\sqrt[n]{b} =\sqrt{144^{2} } *\sqrt{144}$

Now, we will simplify the radical expression:

                        $144*\sqrt{144}$

Now, factor it and rewrite the radicand in exponential form:

                       $144*\sqrt{12^{2} }$

simplify the radical expression: $144*12$

                                               $=1728$

The expression which is equivalent to $144^{\frac{3}{2} }$ is 1728.

What is exponential form form?

The exponential form is an easier way of writing repeated multiplication involving base and exponents. For example, we can write 5 × 5 × 5 × 5 as 54 in the exponential form, where 5 is the base and 4 is the power. In this form, the power represents the number of times we are multiplying the base by itself. 1.

What is the exponential form of 12?

2*2*3 will be its exponential form.

What is the exponential form of 243?

Hence, we have represented 243 as a product of prime given as 243=3×3×3×3×3, and in the exponential form as 243=35.

Learn more about exponential form, refer to:

https://brainly.com/question/4429020

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