Question

Simplify open parentheses x to the two fifths power close parentheses to the 3 sevenths power. • x to the one half power • x to the two sevenths power • x to the three fifths power • x to the six thirty fifths power

Answer 1

The simplified expression is x to the 23/14th power. This result is obtained by sequentially multiplying and adding exponents of x according to the rules of exponents.

Step-by-step explanation:

To simplify the expression (x to the two fifths power) to the 3 sevenths power · x to the one half power · x to the two sevenths power · x to the three fifths power · x to the six thirty fifths power, we apply the rules of exponents. When raising an exponent to another power, we multiply the exponents. When multiplying expressions with the same base, we add the exponents.

Step-by-step explanation:

1. Raise (x2/5) to the power of 3/7 by multiplying the exponents: x(2/5)×(3/7) = x6/35.
2. Multiply x6/35 by x1/2, add the exponents: x6/35 + 35/70 (converted 1/2 to 35/70) = x41/70.
3. Multiply x41/70 by x2/7, add the exponents: x41/70 + 20/70 = x61/70.
4. Multiply x61/70 by x3/5, convert 3/5 to 42/70 and add the exponents: x61/70 + 42/70 = x103/70.
5. Multiply x103/70 by x6/35, convert 6/35 to 12/70 and add the exponents: x103/70 + 12/70 = x115/70.
6. Simplify x115/70 to x23/14 by dividing both numerator and denominator by 5.

The simplified expression is x23/14.

Answer 2

The simplified form of the expression is x^(6/35). Option D, x to the six thirty fifths power, is the correct answer.

Step-by-step explanation:

When simplifying expressions with exponents raised to other exponents, we use the following rule:

(a^m)^n = a^(m * n)

Therefore, in this case:

x^(2/5)^(3/7) = x^(2/5 * 3/7)

Calculating the product of the exponents:

(2/5) * (3/7) = 6/35

Therefore, the simplified form of the expression is x^(6/35), matching option D.

The other options represent incorrect simplifications:

x^(1/2): This ignores the outer exponent of 3/7.

x^(2/7): This only considers the inner exponent of 2/5.

x^(3/5): This multiplies the inner exponents but ignores the outer exponent.

Remember, when dealing with nested exponents, pay close attention to the order of operations and apply the exponent rules correctly for accurate simplification.

Option D is answer.