Exponents and Roots MCQs with Answers & Explanations (Page 2)

When raising a power to another power, you multiply the exponents. Multiplying the inside exponent 3 by the outside exponent 2 yields an exponent of 6, resulting in 2^6.

The power of a power rule dictates that we multiply the inner and outer exponents. Therefore, 4 multiplied by 3 gives 12, making the simplified form x^12.

To simplify a base raised to a power and then raised to another power, multiply the two exponents together. Multiplying 2 and 4 gives 8, resulting in 3^8.

Applying the power rule, we multiply the exponent inside the parentheses by the exponent outside. The product of 5 and 2 is 10, so the expression simplifies to y^10.

When an exponential term is raised to a power, multiply the exponents. Here, multiplying 3 by 3 gives an exponent of 9, leaving us with 5^9.

The rule for a power raised to a power requires multiplying the exponents. Calculating 2 times 6 gives 12, so the expression becomes a^12.

By multiplying the exponents according to the power of a power rule, we calculate 4 * 2 = 8. The base stays the same, resulting in 10^8.

Multiplying the exponent 5 by the outer exponent 3 gives 15. The base remains 4, so the final simplified answer is 4^15.

When a term with an exponent is raised to an additional power, the exponents are multiplied. Multiplying 3 by 5 yields 15, making the simplified term z^15.

Using the power rule, multiply the inner exponent 2 by the outer exponent 2. This gives an exponent of 4, keeping the base 7 intact to form 7^4.

According to the zero exponent rule, any non-zero real number raised to the power of zero is always equal to 1. Therefore, 5^0 equals 1.

Any non-zero variable or number raised to the zero power simplifies to exactly 1. Thus, as long as x is not zero, x^0 = 1.

Because the entire expression (2xy) is enclosed in parentheses and raised to the power of zero, the zero exponent rule applies to the whole term, resulting in 1.

Regardless of how large the base is, any non-zero number raised to the zero power equals 1. Therefore, 100^0 evaluates to 1.

Any non-zero number raised to the power of zero is always equal to 1. The negative sign is inside the parentheses, meaning the entire base of -5 is raised to the zero power, resulting in 1.

A negative exponent means taking the reciprocal of the base and making the exponent positive. So, 2^-3 becomes 1/(2^3), which evaluates to 1/8.

To rewrite a term with a negative exponent, place it in the denominator with a positive exponent. Therefore, x^-2 is equivalent to 1/x^2.

The negative exponent rule dictates that 3^-2 flips the base to the denominator, giving 1/(3^2). Since 3^2 is 9, the final answer is 1/9.

A negative exponent flips the position of the term in a fraction. Changing y^-4 to a positive exponent moves it to the denominator, becoming 1/y^4.

An exponent of -1 indicates the reciprocal of the base number. Therefore, 5^-1 is the reciprocal of 5, which is 1/5.