Solve the following exercise:
Solve the following exercise:
Let's use the definition of root as a power:
when we remember that in a square root (also called "root to the power of 2") we don't write the root's power and:
meaning:
Let's return to the problem and convert using the root definition we mentioned above the root in the fraction's numerator in the problem:
Now let's recall two laws of exponents:
a. The law of exponents for a power applied to a product in parentheses:
b. The law of exponents for a power of a power:
Let's apply these laws to the fraction's numerator in the expression we got in the last step:
where in the first stage we applied the above-mentioned law of exponents noted in a' and applied the power to both factors of the product in parentheses in the fraction's numerator, we did this carefully using parentheses since one of the factors in the parentheses is already raised to a power, in the second stage we applied the second law of exponents mentioned in b' to the second factor in the product,
Let's simplify the expression we got:
where in the first stage we converted back the fraction's power to a root, for the first factor in the product, using the definition of root as a power mentioned at the beginning of the solution, but in the opposite direction,
Additionally- we calculated the product in the exponent of the second factor in the product in the fraction's numerator in the expression we got, then we simplified the resulting fraction in that exponent for that factor.
Let's finish the calculation and simplify the resulting fraction:
Let's summarize the solution steps so far, we got that:
Therefore the correct answer is answer c.