Properties of exponents Rewrite the expression in the form b^n—— (b^2)^3/7

Mathematics

1 answer:

exis [7]2 years ago

3 0

Answer:

$b^{\frac{6}{7}}$ is the required expression.

Step-by-step explanation:

$(b^2)^{\frac{3}{7}}\\\\\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\\\\=b^{2\cdot \frac{3}{7}}\\\\=b^{\frac{6}{7}}$

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Which is the value of the expression ((10^4)(5^2)/(10^3)(5^3))^3

dimulka [17.4K]

Answer:

Step-by-step explanation:

Let's set this up to see if we can simplify it a bit:

$(\frac{10^4*5^2}{10^3*5^3})^3$

Notice we have 4 tens on top and 3 on bottom, so we can eliminate the bottom 3 altogether and leave just one on top. And we have 2 fives on the top and 3 on bottom, so we can eliminate the 2 on the top and leave one on the bottom. Now that looks like this:

$(\frac{10}{5})^3$