Can you please explain to me how I can solve these problems?
(3^ square root of3) ^square root of 3
(x^ square root of 2) ^square root of 7
5^(2)(square root of 3) • 5^(4)(square root of 3)
x^(3)(pi) / x^(pi)
1. (3^sqrt3)^sqrt3 = 3^3 = 27.
2. (X^sqrt2)sqrt7 = X^sqrt(2*7) = X^sqrt14.
3. 5^2sqrt3 * 5^4sqrt3 = 5^6sqrt3.
4. X^3pi / X^pi = X^2pi.
Sure! I can explain how to solve each of these problems step-by-step.
1. (3^ square root of 3) ^ square root of 3:
To simplify this expression, you can multiply the exponents. The square root of 3 raised to the power of square root of 3 is equal to 3. Therefore, the final answer is 3^3, which simplifies to 27.
2. (x^ square root of 2) ^ square root of 7:
Similarly, to simplify this expression, you can multiply the exponents. The square root of 2 raised to the power of square root of 7 is equal to 2. Therefore, the final answer is x^2.
3. 5^(2)(square root of 3) • 5^(4)(square root of 3):
When multiplying exponents with the same base, you can add the exponents. In this case, you add the exponents of 2 and 4, which gives you 6. Therefore, the expression simplifies to 5^(6)(square root of 3).
4. x^(3)(pi) / x^(pi):
To divide exponents with the same base, you can subtract the exponents. In this case, you subtract the exponent of pi from the exponent of 3pi. Therefore, the expression simplifies to x^(3pi - pi), which further simplifies to x^(2pi).
Remember, these explanations provide the steps to solve the given problems. However, it's always important to double-check your calculations and make sure all the laws of exponents are properly applied.