What is 2/3 to the Second power?

What is 2/3 to the Second power?

(2/3) to the second power means raising 2/3 to the exponent 2. To do this, you multiply 2/3 by itself:

(2/3) * (2/3) = 4/9

So, 2/3 to the second power is equal to 4/9.

Powers and Exponents

When we talk about raising a number to a power, we are referring to repeated multiplication of that number by itself. The number being multiplied is called the base, and the number of times it is used in the multiplication is called the exponent or power.

For example: 23 = 2 x 2 x 2 Here, 2 is the base and 3 is the exponent. We would read this as “two to the third power equals eight”.

This works with fractions and decimals as well. For example: (1/2)3 = (1/2) x (1/2) x (1/2) = 1/8

So when we raise a fraction to a power, we multiply the fraction by itself the number of times indicated by the exponent.

Calculating Exponents

To calculate an exponential expression by hand:

1. Write out the base and exponent.
2. Multiply the base by itself the number of times indicated by the exponent.

For example, to calculate 2/3 squared:

1. Write out the expression: (2/3)2
2. Multiply (2/3) x (2/3) = 4/9

So (2/3)2 = 4/9

We can double check this using a calculator. Typing (2/3)^2 into a calculator also returns 4/9.

Properties of Exponents

There are some handy rules and properties that allow us to simplify exponential expressions:

Product Rule: am x an = am+n (a^m)*(a^n) = a^(m+n)

Power Rule: (am)n = amn (a^m)^n = a^(mn)

So for our example: (2/3)2 = (2/3)(2/3) = (22)/(3*3) = 4/9

We were able to reduce the expression by applying the Product Rule. This provides a shortcut for manually multiplying exponential expressions.

In summary, to raise a fraction like 2/3 to a power, we multiply 2/3 by itself the number of times indicated by the exponent. Using properties like the Product Rule can help simplify the calculation. Specifically, (2/3)2 equals 4/9, which we can determine either by manual multiplication or by applying exponential rules and properties.

FAQs

What is 3 to the second power of 3? 3 to the second power of 3 means raising 3 to the power of 2 and then raising the result to the power of 3: (3^2)^3 = 9^3 = 729.

What is 2 3 to the 4th power in fraction form? 2^3 to the 4th power means raising 2 cubed to the 4th power: (2^3)^4 = 8^4 = 4096.

What is 3 raise to the power of 2? 3 raised to the power of 2 is equal to 9.

What is 2 of the second power? 2 to the second power is equal to 4.

Is 3 power 2 equal to 2 power 3? No, 3^2 (3 to the second power) is not equal to 2^3 (2 to the third power). 3^2 = 9, and 2^3 = 8.

How do you calculate powers? To calculate powers, you raise a number (the base) to an exponent. For example, to calculate 2^3, you multiply 2 by itself three times: 2 * 2 * 2 = 8. To calculate powers, you can also use a calculator or software with built-in mathematical functions.