When the power of the base is negative, we can apply the same formula (a m) n = a m n by multiplying the exponents. What is Power of a Power Rule for Negative Exponents? We can simply multiply the powers and keep the base the same. The formula for the power to the power rule is given by, (a m) n = a m n, where a is the base and m, n are the powers, is given by, (a m) n = a m n. The rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.' What is the Formula of Power to the Power Rule? The power of a power rule in exponents is a rule that is applied to simplify an algebraic expression when a base is raised to a power, and then the whole expression is raised to another power. Rational power to the power rule: (a p/q) m/n = a pq/mnįAQs on Power Of a Power Rule What is Power of a Power Rule in Math?.Power of a power rule for negative exponents:.The formula for the power of a power rule is (a m) n = a m n.The power to the power rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.'.We will simply multiply the powers 2/3 and -3/4 keeping the base the same as 3. Solution: To find the value of (3 2/3) -3/4, we will use the power of a power rule for rational exponents. So, we multiply the two powers -5 and 9 to obtain the result and keep the base x the same.Įxample 3: Evaluate the value of (3 2/3) -3/4. Solution: We can observe that the expression (x -5) 9 has a negative power. = 2 10 - Įxample 2: Simplify the expression (x -5) 9 Solution: To simplify the expression (-2 2) 5, we apply the power to the power rule and multiply the powers 2 and 5. Let us solve a few examples and apply the formula to understand its application. Now that we know the formula for the power to the power rule with positive exponents, negative exponents, and rational exponents. Power Of a Power Rule With Negative Exponents We will solve a few examples based on the concept for a better understanding. We will understand the application of the power of a power rule in the simplification of algebraic expressions with negative and rational exponents. To apply power to the power rule, we multiply the two powers keeping the base the same.įurther, in this article, we will explore the power to the power rule in detail and its formula. Now, the power of a power rule is used to simplify expressions of the form (b x) y which on simplification is written as b xy. For the expression b x, b is the base and x is the power (also called the exponent) which implies b is multiplied by itself x times. Before we get into the detail of the concept, let us recall the meaning of power and base.
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