Exponents and Roots MCQs with Answers & Explanations

When multiplying terms with the same base, you add the exponents according to the product rule. Here, the base is 2, so 2^3 * 2^4 becomes 2^(3+4), which equals 2^7.

According to the product rule for exponents, when you multiply two terms with the same base, you add their exponents together. Therefore, x^5 * x^2 is equal to x^(5+2), which simplifies to x^7.

Using the law of exponents for multiplication, we keep the base the same and add the powers. For 3^4 * 3^2, adding the powers 4 and 2 gives us 3^6.

A variable without a visible exponent has an implicit exponent of 1. So, y^6 * y^1 means we add the exponents 6 and 1 together, resulting in y^7.

To multiply expressions with identical bases, you must add the exponents while keeping the base unchanged. Adding 2 and 5 gives an exponent of 7, resulting in 5^7.

The product rule applies to any number of terms with the same base. Adding the exponents 3, 4, and the implicit 1 gives 3 + 4 + 1 = 8, yielding a^8.

When multiplying powers of 10, the base remains 10 and the exponents are summed. The sum of 3 and 4 is 7, making the final expression 10^7.

By applying the fundamental rule of exponents for multiplication, we add the exponents 2 and 3. The base remains 4, which gives us 4^5.

Since the bases are identical, the exponents are simply added together. Taking the sum of 2 and 8 yields 10, resulting in the simplified term z^10.

The product rule tells us to add the exponents when the base is identical. Adding the exponent 1 to the exponent 6 gives a final power of 7, so the answer is 7^7.

When dividing exponential terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. Here, 8 - 3 equals 5, resulting in 2^5.

According to the quotient rule for exponents, we subtract the bottom exponent from the top exponent when bases are the same. Subtracting 4 from 9 gives us x^5.

Using the quotient rule, we keep the base of 3 and subtract the denominator's exponent from the numerator's exponent. The calculation 7 - 2 leaves us with 3^5.

For division of terms with identical bases, subtract the lower power from the upper power. Taking 3 away from 10 gives an exponent of 7, making the answer y^7.

Applying the exponent rule for division, subtract the exponent 4 from the exponent 6 while maintaining the base of 5. This results in 5^2.

Subtracting the exponents 8 - 7 gives 1. Any variable raised to the power of 1 is just the variable itself, so a^1 is written simply as a.

The quotient rule dictates subtracting the denominator's exponent from the numerator's. Performing 5 - 2 yields 3, giving a final simplified expression of 10^3.

Since the bases are the same, we simply subtract the exponents. Subtracting 3 from 9 leaves an exponent of 6, making the simplified form 4^6.

By applying the quotient rule for exponents, we subtract the bottom exponent (5) from the top exponent (12). This operation yields z^7.

Subtracting the exponents gives 8^(4-4) = 8^0. Any non-zero base raised to the power of zero equals 1. Alternatively, any number divided by itself is 1.