Understanding: Powers with the Same Exponent

# Understanding: Powers with the Same Exponent Video Lecture | Mathematics (Maths) Class 7

## Mathematics (Maths) Class 7

76 videos|345 docs|39 tests

## FAQs on Understanding: Powers with the Same Exponent Video Lecture - Mathematics (Maths) Class 7

 1. What is the definition of powers with the same exponent?
Ans. Powers with the same exponent refer to numbers that are raised to the same power or have the same exponent. For example, if we have the numbers 2, 3, and 4, and we raise them to the power of 2, we get 2^2, 3^2, and 4^2 respectively. In this case, the exponent is 2, and the numbers have the same exponent.
 2. How do you simplify powers with the same exponent?
Ans. To simplify powers with the same exponent, you need to apply the exponent to each number individually. For instance, if we have 2^3, 4^3, and 6^3, all raised to the power of 3, we simplify them as (2^3)^3, (4^3)^3, and (6^3)^3. Then, we can further simplify it as 2^(3*3), 4^(3*3), and 6^(3*3), which eventually results in 2^9, 4^9, and 6^9 respectively.
 3. Can powers with the same exponent have different bases?
Ans. Yes, powers with the same exponent can have different bases. The exponent only affects the individual numbers or bases it is applied to. For example, if we have 2^4 and 3^4, both raised to the power of 4, they would simplify as 2^(4*4) and 3^(4*4), which further simplifies to 2^16 and 3^16 respectively.
 4. What is the significance of powers with the same exponent in mathematics?
Ans. Powers with the same exponent are significant in mathematics as they allow us to compare and analyze numbers with a common power. It helps in understanding the relationships between different numbers and their exponential growth or decay. Powers with the same exponent also play a crucial role in various mathematical operations and formulas.
 5. How can powers with the same exponent be used in real-life scenarios?
Ans. Powers with the same exponent can be used in real-life scenarios to analyze and compare quantities that undergo exponential growth or decay. For example, in finance, powers with the same exponent can be used to calculate compound interest over time. In science, they can be used to model population growth, radioactive decay, or the decay of certain substances. Additionally, powers with the same exponent are also used in fields such as engineering and computer science for various calculations and simulations.

## Mathematics (Maths) Class 7

76 videos|345 docs|39 tests

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