Emily explains
3^2/3 *6^√3^3=3^2/3*3^3/6=3^6/18=3^√3
is emily correct? Justify your answer
No, Emily is not correct.
When simplifying exponents, we need to apply the rules of exponents.
In this case, we have:
3^(2/3) * 6^(√3^3)
Using the rule that (a^m)*(a^n) = a^(m+n), we can rewrite the expression as:
3^(2/3 + √3^3)
Now, we evaluate √3^3. The square root of a number is the same as raising the number to the power of 1/2. So, √3^3 = (3^(3/2))
We can now rewrite the expression as:
3^(2/3 + (3^(3/2)))
Since the bases are different (3 and 3^(3/2)), we cannot combine the exponents. Therefore, Emily's simplification is not correct.