Let's start by breaking it down;
The base is the standard whole number in which we are going to multiply to the X power. Here, the X: Xy.
The power, or exponent, often displayed in superscript (or small and to the top right of the base number, as displayed above), and occasionally using a caret: X^Y, or rarely as a double multiplication symbol X**Y.
Here's an example:
24 * 25
As we learned, the base here is 2, and the powers are 4 and 5.
When you are presented with an equation like this, the purpose is generally to not find out what all of that equals, but to combine the two sides into one, like algebra!
To do this, you could multiply it out and do it all the long way, but there's a trick! All you have to do is simply add the two exponents.
24 * 25 is the same as 24 + 5, which would equal 29.
When multiplying powers with the same base, you add the exponents: (a^m \times a^n = a^{m+n}). Conversely, when dividing powers with the same base, you subtract the exponents: (a^m \div a^n = a^{m-n}). This rule applies as long as the base (a) is not zero.
If you are multiplying powers of the same base (like 24 times 211), yes, you add the exponents.
When multiplying powers with the same base, you add the exponents due to the properties of exponents that define multiplication. This is based on the idea that multiplying the same base repeatedly involves combining the total number of times the base is used. For example, (a^m \times a^n = a^{m+n}) because you are effectively multiplying (a) by itself (m) times and then (n) times, resulting in a total of (m+n) multiplications of (a). This rule simplifies calculations and maintains consistency in mathematical operations involving exponents.
To multiply powers with the same base, you simply add their exponents. For example, if you have ( a^m \times a^n ), the result is ( a^{m+n} ). This rule applies as long as the bases are identical.
When multiplying exponents with the same base add them: x^3*x^2 = x^5 When dividing exponents with the same base subtract them: x^3/x^2 = x^1 or x
When multiplying powers with the same base, you add the exponents: (a^m \times a^n = a^{m+n}). Conversely, when dividing powers with the same base, you subtract the exponents: (a^m \div a^n = a^{m-n}). This rule applies as long as the base (a) is not zero.
If you are multiplying powers of the same base (like 24 times 211), yes, you add the exponents.
When multiplying powers with the same base, you add the exponents due to the properties of exponents that define multiplication. This is based on the idea that multiplying the same base repeatedly involves combining the total number of times the base is used. For example, (a^m \times a^n = a^{m+n}) because you are effectively multiplying (a) by itself (m) times and then (n) times, resulting in a total of (m+n) multiplications of (a). This rule simplifies calculations and maintains consistency in mathematical operations involving exponents.
To multiply powers with the same base, you add the exponents. For example, 10^2 x 10^3 = 10^5. Similarly, to divide powers with the same base, you subtract the exponents. For example, 10^3 / 10^5 = 10^(-2).
Add the powers: eg 3 squared times 3 cubed = 3 to the fifth More generally, if b is the base (bx )(by )=bx+y
To multiply powers with the same base, you simply add their exponents. For example, if you have ( a^m \times a^n ), the result is ( a^{m+n} ). This rule applies as long as the bases are identical.
What do you mean by product of powers?Is that what you mean?am * an = a(m+n).The above is only valid when the base (a) is same for both the expressions.
Add the indices
I presume you mean you are multiplying two powers of the same base, where both exponents are negative. Regardless of the signs of the exponents, you algebraically add the exponents. For example, 2-3 times 2-4 is 2-7; 35 times 3-8 is 3-3.
When multiplying exponents with the same base add them: x^3*x^2 = x^5 When dividing exponents with the same base subtract them: x^3/x^2 = x^1 or x
10 to the power of 15 when multiplying items with the same base (in this case 10) you simply add the powers
You add them.