When multiplying numbers with the same base and different or same exponents, the product is the base to the power of the sum of the exponents of the multiplicands.
Examples:
52 x 57 x 510 = 519
n x n4 = n5
75 ÷ 72 = 75 x 7-2 = 73
22 x √2 = 22 x 20.5 = 22.5
As a product of its prime factors in exponents: 24*32*11 = 1584
how can exponent can make it easier to write an expression with a repeated factor in the product
As a product of its prime factors in exponents: 23*32*52 = 1800 Or expressed in scientific notation: 1.8*103
As a product of its prime factors in exponents: 2^6 times 5^6 = 1,000,000 As in terms of scientific notation it is: 1.0*10^6
The base is the repeated factor, the exponent is the number of times by which the base is mutltiplied by itself. The exponent is also known as the power, althought the product of the exponential expression can also be described as the power.
when two numbers are multiplied together that are exponents you multiply the bases amd add the exponents the relationship would simply be that the product exponents are the sum of the exponents being multiplied in the question
The exponent of the base is a step to solve the problems now the exponent of the product will also adjust a step to solve the equation but it contains more cooperative need.
Rules for exponents to multiply powers, add the exponents to divide powers, subtract the exponents to find a power of a power, multiply the exponents to find a power of a quotient, apply the power top and bottom to find a power pf a product, apply the exponent to each factor in the product x0 = 1 anything to the power zero equals one x-a = 1/xa a negative exponent means "one over" the positive exponent
As a product of its prime factors in exponents: 24*32*11 = 1584
how can exponent can make it easier to write an expression with a repeated factor in the product
Monomials can have negative exponents, if the term for the exponent is not a variable, but if it is a variable with a negative exponent, the whole expression will not be classified. This is so because the definition of a monomial states that, a monomial can be a product of a number and one or more variables with positive integer exponents. I hope that answered your question!
As a product of its prime factors in exponents: 25*52 = 800 Or as: 8.0*102 in scientific notation
As a product of its prime factors in exponents: 23*32*52 = 1800 Or expressed in scientific notation: 1.8*103
I can think of two: - To multiply powers with the same base, add the exponents: (a^b)(a^c) = a^(b+c). - To find a power of a product, apply the exponent to each factor in the product: (ab)^c = (a^c)(b^c).
As a product of its prime factors in exponents: 2^4 times 3^2 times 7 = 1008
As a product of its prime factors in exponents: 2^6 times 5^6 = 1,000,000 As in terms of scientific notation it is: 1.0*10^6
If x2 and x3 are meant to represent x2 and x3, then x2 times x3 = x5 You find the product of exponent variables by adding the exponents.