Which expression is equivalent to (x^6 x x^10) and why?
A x^-20 , because first you multiply the exponents in the numerator and then divide by the exponent in the denominator.
B x^21, because first you add the exponents in the numerator and then subtract by the exponent in the denominator, and then add the new exponents using the power of the power property.
C x^38, because first you add the exponents in the numerator and then subtract by the exponent in the denominator, and then multiply the new exponents using the power of the power property.
D x^26 , because first you multiply each exponent by two using the power of a power property, then you add the new exponents in the numerator and subtract by the new exponent in the denominator
The correct answer is D x^26.
This is because the expression (x^6 x x^10) can be simplified using the product of powers property, which states that when you multiply two terms with the same base, you add their exponents.
In this case, x^6 can be written as x^6 * x^1 (since any number raised to the power of 1 is still the same number), and x^10 can be written as x^10 * x^0 (since any number raised to the power of 0 is equal to 1).
So, combining the exponents, we get x^(6+1) * x^(10+0) = x^7 * x^10 = x^(7+10) = x^17.
Therefore, the expression (x^6 x x^10) is equivalent to x^17.
None of the given answer choices is correct.