3^7⋅3^−9=
To solve this, we can use the exponent rule that says when you multiply two numbers with the same base, you add the exponents.
So, we have 3^7 * 3^-9
Adding the exponents, we get 3^(7 + (-9))
Simplifying, 7 + (-9) is -2
Therefore, 3^7 * 3^-9 becomes 3^(-2).
Hence, 3^7 * 3^-9 = 3^(-2).
To calculate 3^7⋅3^−9, we need to remember the rule of exponents that says "a^m⋅a^n = a^(m+n)."
In this case, we have 3^7⋅3^−9. Applying the rule, we can combine the exponents:
3^7⋅3^−9 = 3^(7 + -9)
Next, we simplify the exponent:
3^(-9) means 1/3^9
Therefore, 3^(7 + -9) = 3^(7 - 9) = 3^(-2)
To calculate 3^(-2), we use another exponent rule, which states that "a^(-n) = 1/a^n."
Using this rule, we can rewrite 3^(-2) as 1/3^2:
3^(-2) = 1/3^2 = 1/9
Therefore, 3^7⋅3^−9 = 1/9.
To find the value of 3^7 ⋅ 3^(-9), we can simplify it using the laws of exponents.
The law of exponents states that when multiplying two numbers with the same base, you can add their exponents.
In this case, we have the base 3, so we can add the exponents 7 and -9.
The sum of 7 and -9 is -2.
Therefore, 3^7 ⋅ 3^(-9) simplifies to 3^(-2), or 1/3^2.
So, 3^7 ⋅ 3^(-9) = 1/3^2.